Pith. sign in

REVIEW 2 major objections 6 minor 2 cited by

Stellar-mass black holes born in nuclear star clusters rarely grow into heavy seeds while their birth gas is still present.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-14 23:29 UTC pith:MP5COJWU

load-bearing objection Solid in-situ light-seed MHD suite: under fiducial f_acc=0.05 they stall at ~400–500 M⊙; the heavy-seed outcome flips only when f_acc ≳ 0.5, which the paper itself maps. the 2 major comments →

arxiv 2603.10581 v2 pith:MP5COJWU submitted 2026-03-11 astro-ph.GA

The In Situ Growth of Stellar-mass "Light" Seed Black Holes in Nuclear Star Clusters

Yanlong Shi , Norman Murray This is my paper
classification astro-ph.GA
keywords light seed black holesnuclear star clustersvery massive starsBondi accretionstellar feedbackgiant molecular cloudssupermassive black hole seedsmultiple-generation star formation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks whether the black-hole leftovers of the most massive stars can grow into intermediate-mass or supermassive black holes using only the gas left inside the giant molecular cloud that formed them. Using magnetohydrodynamic simulations that resolve very massive stars, their winds and explosions, and the subsequent black-hole accretion, the authors show that stellar feedback empties the dense gas reservoir within a few million years. Remnant black holes do form and sink to the cluster center, and a few direct-collapse objects briefly accrete above the Eddington rate, yet under the authors’ standard sub-grid model they stop at only a few hundred solar masses. Only if a large fraction of the Bondi inflow is allowed to reach the black hole does runaway growth to a million solar masses become possible. The result matters because it implies that light seeds need later, larger-scale gas inflows or dynamical processes if they are to explain the earliest quasars.

Core claim

With the fiducial sub-grid accretion and feedback model, in-situ growth of stellar-mass remnant black holes inside their birth giant molecular clouds is inefficient: even the most successful direct-collapse seeds reach only about 400–500 solar masses before the remaining gas is expelled by stellar feedback. Runaway growth to roughly a million solar masses occurs only when the model is altered to let a high fraction of Bondi inflow reach the black hole.

What carries the argument

The FIRE+VMS hybrid scheme that splits stars above 50–100 solar masses into individually tracked very-massive-star particles (with PARSEC evolutionary tracks, radiative and mechanical feedback, and remnant formation) while treating lower-mass stars as single stellar populations, then applies Bondi–Hoyle accretion with a free capture fraction f_acc and bipolar mechanical feedback onto the newly formed black holes.

Load-bearing premise

The fraction of Bondi inflow that actually reaches the black hole is fixed at a few percent without independent calibration; raising that fraction above roughly one-half reverses the entire conclusion about whether heavy seeds can form.

What would settle it

A resolved simulation or observation of super-Eddington accretion onto a stellar-mass black hole embedded in a dense, magnetized core that measures a capture fraction of order 0.5 or higher, or a clear detection of an intermediate-mass black hole still inside a young, gas-rich nuclear star cluster younger than 10 Myr.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper uses MHD simulations (GIZMO + FIRE-3 with a hybrid FIRE+VMS treatment of stars above m_cut) of star-forming GMCs (10^5–10^9 M_⊙, Σ ~ 10^3–10^4 M_⊙ pc^{-2}) to form compact clusters and track in-situ remnant BHs from resolved VMSs. With the fiducial sub-grid model (Bondi accretion with f_acc = 0.05 and bipolar winds at 3000 km s^{-1}), stellar feedback clears dense gas after ~few free-fall times; remnant BHs form ~3 Myr after the starburst, concentrate at the center, and grow only modestly (to ~400–500 M_⊙ for a few DCBHs above the PISN gap at low Z). Top-heavy IMF and natal kicks do not produce heavy seeds. Runaway growth to ~10^6 M_⊙ appears only when f_acc ≳ 0.5. The authors also note a correlation with multi-generation star formation in the most massive, extended clouds.

Significance. The work is a useful step beyond earlier studies that inserted pre-existing seeds: it self-consistently forms light seeds from VMS evolution and feedback inside GMC-scale clusters that resemble high-z nuclear star clusters. The suite spans mass, radius, metallicity, IMF, and kicks, and the negative result (no heavy seeds at f_acc = 0.05) is robust inside that model. The explicit f_acc/v_wind exploration in §4.1 and Figure 7 is a strength: it makes the model dependence transparent rather than hidden. If the fiducial microphysics is approximately correct, the paper constrains in-situ light-seed growth on ~10 Myr timescales and motivates cosmological follow-ups with larger-scale inflows.

major comments (2)
  1. §2.3 and §4.1 (and Figure 7): the central claim that in-situ accretion is inefficient for heavy seeds is true only for f_acc ≲ 0.05. When f_acc ≳ 0.5 a few seeds reach ~10^6 M_⊙ via runaway Bondi growth. The paper correctly flags this, but the abstract and conclusions still lead with the negative result as if it were the physical outcome. The abstract and §5 should state more prominently that the no-heavy-seed conclusion is conditional on the unconstrained capture fraction, and should cite the slim-disk / super-Eddington literature that motivates why f_acc could be higher.
  2. §2.3: f_acc and v_wind lack independent calibration from resolved accretion-flow simulations or X-ray binary winds. Given that the entire heavy-seed conclusion flips across the explored range, the paper should either (i) adopt a physically motivated range for f_acc (e.g., from Jiang et al. 2014, Zhang et al. 2025) as the baseline rather than a single fiducial 0.05, or (ii) reframe the main result as a mapping from (f_acc, v_wind) to final BH mass rather than a single negative statement.
minor comments (6)
  1. Figure 2: BHFR is defined as dM_BH,tot/dt; clarify whether this is the instantaneous formation rate of new remnants or includes subsequent accretion (the text suggests the former).
  2. Figure 3: some density profiles are noisy because no regular globular cluster forms; consider marking those runs or using a different centering metric for open-cluster cases.
  3. §2.2.1 / Eq. (1): the mass-loss fit is given without a stated validity range in m and Z; a brief note on the PARSEC coverage would help reproducibility.
  4. §4.2: the multi-generation / BH-accretion correlation is interesting but remains qualitative; a simple quantitative metric (e.g., fraction of stars with Z_⋆ > 2 Z_ini vs. max ΔM_BH) would strengthen the claim.
  5. Table 1 and notation: the M%e_R%e_Z%e naming is clear in the text but could be defined once in the table caption for readers skimming.
  6. A few typographical issues: “arXiv:2603.10581v1” date formatting; occasional missing spaces around ~ and ×; “Godzilla” cluster citation is fine but ensure Pascale & Dai (2024) is consistently formatted.

Circularity Check

0 steps flagged

No significant circularity; conclusions are direct numerical outcomes of forward MHD simulations with explicit free parameters and variations, not reductions by construction.

full rationale

The paper's derivation chain consists of constructing GMC initial conditions (following prior methodology but with new in-situ VMS resolution), evolving them under the hybrid FIRE+VMS framework (PARSEC tracks for mass loss/feedback, Bondi accretion with free f_acc and v_wind), and reporting the resulting BH mass spectra and accretion histories. The central claim—that fiducial f_acc=0.05 yields only ~400–500 M_⊙ seeds while f_acc ≳ 0.5 permits runaway to ~10^6 M_⊙—is obtained by running the simulations and inspecting the outputs (Figs. 4–7, §3–4); it is not forced by definition, by a fit to the target quantity, or by a self-citation that itself encodes the result. Self-citations (Shi et al. 2023, 2024a,b) supply environmental context and IC recipes but are not load-bearing uniqueness theorems or ansatzes that define the present outcome. f_acc is openly treated as an unconstrained sub-grid parameter whose sensitivity is mapped rather than hidden. No self-definitional loop, fitted-input-as-prediction, or renaming of a known result appears.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 1 invented entities

The central claim is a numerical outcome of MHD + sub-grid star/BH physics. Load-bearing free parameters are the Bondi capture fraction and wind speed; domain assumptions include the Bondi formula, FIRE feedback, and PARSEC remnant masses. No new physical entities are postulated; the hybrid FIRE+VMS scheme is a methodological construct.

free parameters (6)
  • f_acc (Bondi capture fraction) = 0.05 (fiducial)
    Fraction of Bondi inflow assumed to reach the event horizon; fiducial 0.05, scanned over 0.005–1. Entire heavy-seed conclusion depends on this choice (§2.3, §4.1).
  • v_wind (BH mechanical wind terminal velocity) = 3000 km/s
    Terminal speed of bipolar BH outflow; fiducial 3000 km/s, also tested at 300 and 30000 km/s. Affects suppression of accretion at fixed f_acc.
  • m_cut (VMS resolution threshold) = 100 M_⊙ (50 M_⊙ for M_cl ≤ 10^6 M_⊙)
    Stars above m_cut are resolved individually; set to 100 M_⊙ (or 50 M_⊙ for low-mass clouds). Controls which objects become tracked remnant BHs.
  • natal kick velocity distribution = log-uniform [0.1, 100] km/s
    Log-uniform kicks in [0.1, 100] km/s assumed 'moderate'; not observationally fixed. Affects retention in shallow potentials.
  • IMF high-mass slope = −2.3 (fiducial); −1.3 (variant)
    Canonical Kroupa slope −2.3 vs top-heavy −1.3; both are hand-chosen variants, not fitted to these data.
  • initial GMC surface density and virial parameters = Σ ≈ 1.3×10^3 or 1.3×10^4 M_⊙ pc^{-2}
    Σ ~ 10^3–10^4 M_⊙ pc^{-2}, kinetic energy = 100% of binding energy, magnetic energy = 1%; set by construction of ICs.
axioms (6)
  • domain assumption Bondi–Hoyle–Lyttleton formula correctly estimates the large-scale inflow rate onto stellar-mass BHs in turbulent, magnetized GMC gas.
    Used as the sole accretion estimator in §2.3 because m_gas ≳ M_BH precludes discrete swallowing.
  • domain assumption FIRE-3 radiative and mechanical feedback prescriptions (including multi-band radiation, SN energy 10^51 erg, and momentum coupling) adequately model gas expulsion in compact GMCs.
    Entire gas-clearing result rests on FIRE-3 loops applied to both SSPs and VMSs (§2).
  • domain assumption PARSEC v2.0 evolutionary tracks correctly predict VMS lifetimes, mass loss, PISN mass gap, and remnant masses as functions of m_ZAMS and Z.
    Remnant mass spectrum and DCBH identification in §2.2 and §3.1 come directly from these tables.
  • domain assumption Slim-disk radiative efficiency (ε_r ~ 0.1 at low Ṁ, dropping to ~0.01 at super-Eddington) correctly sets BH radiative feedback.
    Adopted from Madau et al. (2014) in §2.3; affects photon trapping and heating.
  • ad hoc to paper A hybrid split of the IMF into resolved VMSs and IMF-corrected FIRE SSPs conserves mass, momentum, and feedback without double-counting.
    Methodological construction of §2.1; not a standard library feature of FIRE.
  • domain assumption Sub-grid dynamical friction (Ma et al. 2023) adequately captures sinking of VMSs when low-mass stars are represented as SSPs.
    Applied in §2.2.3 to concentrate massive stars and BHs at cluster centers.
invented entities (1)
  • FIRE+VMS hybrid stellar population scheme no independent evidence
    purpose: Resolve individual VMSs (and their remnant BHs) while retaining FIRE SSP treatment for lower-mass stars, enabling in-situ light-seed formation at GMC scales.
    Methodological construct introduced in §2.1; not a new physical particle or force. Independent evidence is limited to consistency checks against full STARFORGE-style resolution, which is not performed here.

pith-pipeline@v1.1.0-grok45 · 24808 in / 3948 out tokens · 34217 ms · 2026-07-14T23:29:35.328692+00:00 · methodology

0 comments
read the original abstract

Remnant black holes (BHs) of massive stars (``light seeds'') are a potential origin for supermassive black holes (SMBHs). We use magnetohydrodynamic simulations to study the formation and growth of light seeds in star-forming giant molecular clouds (GMCs) with masses $10^5$--$10^9\,M_\odot$, which evolve for $\sim 10$--$30\,\rm Myr$ and form compact star clusters, akin to high-redshift nuclear star clusters. In particular, the simulations resolve very massive stars (VMSs, 100--$300\,M_\odot$), including their radiative and mechanical feedback, and model feedback-regulated accretion onto remnant BHs. We find that, even in compact GMCs capable of forming deep potential wells, the gas reservoir is expelled by sustained stellar feedback and rapidly dispersed after supernova explosions. Remnant BH populations emerge $\sim 3\,\rm Myr$ after the starburst and concentrate at the cluster center (where $\rho_{\rm BH}\sim 10^4$--$10^6\,M_\odot\,{\rm pc}^{-3}$). With our fiducial sub-grid BH accretion/feedback model, in-situ BH accretion is inefficient for forming heavy seeds: some direct-collapse BHs briefly accrete at $\sim$(1--10)$\times$ the Eddington rate, but they reach only $\sim 400$--$500\,M_\odot$. A top-heavy initial mass function or natal kicks do not change this conclusion. Runaway accretion is only possible if the sub-grid BH model allows a high fraction of Bondi inflow to reach the BH, in which case a few seeds can grow to $\sim 10^6\,M_\odot$. We also discuss multiple-generation star formation that may be intrinsically correlated with remnant BH accretion.

Figures

Figures reproduced from arXiv: 2603.10581 by Norman Murray, Yanlong Shi.

Figure 1
Figure 1. Figure 1: Treatment of stellar evolution and feedback in this work (also see Shi et al. 2025), which splits resolved VMSs (with mZAMS > mcut, here mcut = 100 M⊙) from FIRE SSPs following the IMF. The VMS sub-grid model tracks four phases: (a) hydrogen-burning, (b) Wolf-Rayet, (c) supernova, (d) remnant BH formation and feedback￾regulated accretion. Meanwhile, FIRE SSPs evolve with an IMF correction to avoid double-c… view at source ↗
Figure 2
Figure 2. Figure 2: Star formation rate (SFR; dashed) and BH formation rate (BHFR; solid) throughout the evolution of each simulation. Here, BHFR is defined as the rate that VMSs turn into remnant BHs at the end of their life. GMCs with different masses and radii. For each IC, vari￾ations in metallicity, IMF, and natal kicks are displayed in the same panel. Comparing the SFR in absolute time (in Myr) and free-fall times (tff)… view at source ↗
Figure 3
Figure 3. Figure 3: Density profiles of the final star cluster and “BH cluster.” Each density profile is calculated by setting the center xcenter from the minimum of the potential field, as a function of rcl ≡ |x − xcenter|. Note that some curves are noisy since no regular-shaped globular clusters form in these simulations. ∼ 105 M⊙ pc−3 for BHs. The outer density profile of all clusters is well approximated by ρ(r) ∝ r −7/2 … view at source ↗
Figure 4
Figure 4. Figure 4: Mass spectrum of remnant BHs at the end of the simulation for different simulations. In different panels, we vary the metallicity from Z⊙ (Z1) to 0.01Z⊙ (Z0.01). low-metallicity (0.01Z⊙) and massive (≳ 200 M⊙) pro￾genitor stars. After a stellar evolution phase (dashed) lasting ∼ 3 Myr, the stars collapse into BHs (solid) and undergo a short episode of super-Eddington accre￾tion. In the M1e7_R50_Z0.01 run, … view at source ↗
Figure 5
Figure 5. Figure 5: Mass accretion history of selected remnant BHs. Here we present two simulation runs, M1e7_R50_Z0.01 (top) and M1e9_R500_Z0.01 (bottom). Left.–Remnant BH mass at formation versus the accreted mass, where 5 BHs with the most accretion are emphasized with colored circles. Middle.–The mass evolution of the selected stars and their remnants (matching the colors to the left panels). Right.–The accretion rate of … view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of gas morphology and positions of BHs (green or dark dots) in simulations. Top row.– Simula￾tion M1e7_R50_Z0.01 at different stages (left to right: early collapse of the GMC; remnant BH appearance; disruption of the gas reservoir). Bottom row and inset panels.– Similar but for M1e9_R500_Z0.01. The inset panels focuses on a BH undergoing rapid accretion, which is embedded in a turbu￾lent, mag… view at source ↗
Figure 7
Figure 7. Figure 7: Tests with BH mechanical feedback models based on the cloud M1e9_R500_Z0.01. We plot the cumulative dis￾tribution of the final BH mass MBH (top) and the accreted mass ∆MBH of each BH (bottom). For each test, we keep all fiducial setups except facc (0.005, 0.05, 0.5) and vwind (300, 3000, 3000 km s−1 ). Additionally, we test with facc = 1 and all BH feedback disabled (black dot dashed). hibits a population … view at source ↗
Figure 8
Figure 8. Figure 8: The metallicity of stars. Top.– Evolution of the stellar metallicity at formation (Z⋆), for clouds of Z⊙ (Z1; left), 0.1Z⊙ (Z0.1; middle), and 0.01Z⊙ (Z0.01; right). Bottom.– Cumulative distribution of Z⋆ at the end of the simulation. The bottom row shows the cumulative distribution of Z⋆ at the end of the simulation. Comparing differ￾ent clouds, we find that M1e9_R500 exhibits the highest level of multipl… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Predicting intermediate-mass black hole formation in star clusters with machine learning

    astro-ph.GA 2026-05 unverdicted novelty 7.0

    Machine learning regressors trained on Rapster simulations forecast that globular clusters rarely host black holes above 100 solar masses while a few nuclear star clusters may exceed this threshold.

  2. Pebbles to Gems: Intermediate-mass black holes in the first star clusters

    astro-ph.GA 2026-07 conditional novelty 6.0

    Pop. III star clusters form IMBHs peaking at ~200 M⊙ (n~0.2–5 cMpc⁻³) by z~19, with dense massive systems producing up to ~6200 M⊙ seeds at high retention.

Reference graph

Works this paper leans on

71 extracted references · 7 canonical work pages · cited by 2 Pith papers · 1 internal anchor

  1. [1]

    A., Wise, J

    Alvarez, M. A., Wise, J. H., & Abel, T. 2009, ApJL, 701, L133, doi: 10.1088/0004-637X/701/2/L133

    doi:10.1088/0004-637x/701/2/l133 2009

  2. [2]

    P., Agertz, O., Renaud, F., & Teyssier, R

    Andersson, E. P., Agertz, O., Renaud, F., & Teyssier, R. 2023, MNRAS, 521, 2196, doi: 10.1093/mnras/stad692

    doi:10.1093/mnras/stad692 2023

  3. [3]

    P., Rey, M

    Andersson, E. P., Rey, M. P., Pontzen, A., et al. 2025, ApJ, 978, 129, doi: 10.3847/1538-4357/ad99d6 Arca Sedda, M., Mapelli, M., Benacquista, M., & Spera, M. 2023, MNRAS, 520, 5259, doi: 10.1093/mnras/stad331

    doi:10.3847/1538-4357/ad99d6 2025

  4. [4]

    2018, ARA&A, 56, 83, doi: 10.1146/annurev-astro-081817-051839

    Bastian, N., & Lardo, C. 2018, ARA&A, 56, 83, doi: 10.1146/annurev-astro-081817-051839

    doi:10.1146/annurev-astro-081817-051839 2018

  5. [5]

    C., Volonteri, M., & Rees, M

    Begelman, M. C., Volonteri, M., & Rees, M. J. 2006, MNRAS, 370, 289, doi: 10.1111/j.1365-2966.2006.10467.x

    doi:10.1111/j.1365-2966.2006.10467.x 2006

  6. [6]

    1952, MNRAS, 112, 195, doi: 10.1093/mnras/112.2.195

    Bondi, H. 1952, MNRAS, 112, 195, doi: 10.1093/mnras/112.2.195

    doi:10.1093/mnras/112.2.195 1952

  7. [7]

    2003, ApJ, 596, 34, doi: 10.1086/377529

    Bromm, V., & Loeb, A. 2003, ApJ, 596, 34, doi: 10.1086/377529

    doi:10.1086/377529 2003

  8. [8]

    1943, ApJ, 97, 255, doi: 10.1086/144517

    Chandrasekhar, S. 1943, ApJ, 97, 255, doi: 10.1086/144517

    doi:10.1086/144517 1943

  9. [9]

    R., McLeod, A

    Chevance, M., Krumholz, M. R., McLeod, A. F., et al. 2023, in Astronomical Society of the Pacific Conference

    2023

  10. [10]

    534, Protostars and Planets VII, ed

    Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka, Y. Aikawa, T. Muto, K. Tomida, & M. Tamura, 1, doi: 10.48550/arXiv.2203.09570

    Pith/arXiv arXiv doi:10.48550/arxiv.2203.09570

  11. [11]

    2021a, MNRAS, 502, 700, doi: 10.1093/mnras/stab061

    Chon, S., Hosokawa, T., & Omukai, K. 2021a, MNRAS, 502, 700, doi: 10.1093/mnras/stab061

    doi:10.1093/mnras/stab061

  12. [12]

    2020, MNRAS, 494, 2851, doi: 10.1093/mnras/staa863 —

    Chon, S., & Omukai, K. 2020, MNRAS, 494, 2851, doi: 10.1093/mnras/staa863 —. 2025, MNRAS, 539, 2561, doi: 10.1093/mnras/staf598

    doi:10.1093/mnras/staa863 2020

  13. [13]

    2021b, MNRAS, 508, 4175, doi: 10.1093/mnras/stab2497

    Chon, S., Omukai, K., & Schneider, R. 2021b, MNRAS, 508, 4175, doi: 10.1093/mnras/stab2497

    doi:10.1093/mnras/stab2497

  14. [14]

    G., Bressan, A., et al

    Costa, G., Shepherd, K. G., Bressan, A., et al. 2025, A&A, 694, A193, doi: 10.1051/0004-6361/202452573 Del Santo, M., Pinto, C., Marino, A., et al. 2023, MNRAS, 523, L15, doi: 10.1093/mnrasl/slad048 Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604, doi: 10.1038/nature03335

    doi:10.1051/0004-6361/202452573 2025

  15. [15]

    J., H´ enault-Brunet, V., Gieles, M., & Baumgardt, H

    Dickson, N., Smith, P. J., H´ enault-Brunet, V., Gieles, M., & Baumgardt, H. 2024, MNRAS, 529, 331, doi: 10.1093/mnras/stae470

    doi:10.1093/mnras/stae470 2024

  16. [16]

    2025, Nature Astronomy, 9, 1553, doi: 10.1038/s41550-025-02592-w

    Fujimoto, S., Ouchi, M., Kohno, K., et al. 2025, Nature Astronomy, 9, 1553, doi: 10.1038/s41550-025-02592-w

    doi:10.1038/s41550-025-02592-w 2025

  17. [17]

    E., Strader, J., & Ho, L

    Greene, J. E., Strader, J., & Ho, L. C. 2020, ARA&A, 58, 257, doi: 10.1146/annurev-astro-032620-021835 Grudi´ c, M. Y., Guszejnov, D., Hopkins, P. F., et al. 2018a, MNRAS, 481, 688, doi: 10.1093/mnras/sty2303 Grudi´ c, M. Y., Guszejnov, D., Hopkins, P. F., Offner, S. S. R., & Faucher-Gigu` ere, C.-A. 2021, MNRAS, 506, 2199, doi: 10.1093/mnras/stab1347 Gru...

    doi:10.1146/annurev-astro-032620-021835 2020

  18. [18]

    M., Kim, C.-G., & Quataert, E

    Guo, M., Stone, J. M., Kim, C.-G., & Quataert, E. 2023, ApJ, 946, 26, doi: 10.3847/1538-4357/acb81e G¨ urkan, M. A., Freitag, M., & Rasio, F. A. 2004, ApJ, 604, 632, doi: 10.1086/381968

    doi:10.3847/1538-4357/acb81e 2023

  19. [19]

    Y., Hopkins, P

    Guszejnov, D., Grudi´ c, M. Y., Hopkins, P. F., Offner, S. S. R., & Faucher-Gigu` ere, C.-A. 2021, MNRAS, 502, 3646, doi: 10.1093/mnras/stab278

    doi:10.1093/mnras/stab278 2021

  20. [20]

    F., & Ma, X

    Guszejnov, D., Hopkins, P. F., & Ma, X. 2017, MNRAS, 472, 2107, doi: 10.1093/mnras/stx2067

    doi:10.1093/mnras/stx2067 2017

  21. [21]

    Hansen, B. M. S., & Phinney, E. S. 1997, MNRAS, 291, 569, doi: 10.1093/mnras/291.3.569 14

    doi:10.1093/mnras/291.3.569 1997

  22. [22]

    Hopkins, P. F. 2015, MNRAS, 450, 53, doi: 10.1093/mnras/stv195

    doi:10.1093/mnras/stv195 2015

  23. [23]

    F., Grudi´ c, M

    Hopkins, P. F., Grudi´ c, M. Y., Wetzel, A., et al. 2020, MNRAS, 491, 3702, doi: 10.1093/mnras/stz3129

    doi:10.1093/mnras/stz3129 2020

  24. [24]

    F., Kereˇ s, D., O˜ norbe, J., et al

    Hopkins, P. F., Kereˇ s, D., O˜ norbe, J., et al. 2014, MNRAS, 445, 581, doi: 10.1093/mnras/stu1738

    doi:10.1093/mnras/stu1738 2014

  25. [25]

    F., Quataert, E., & Murray, N

    Hopkins, P. F., Quataert, E., & Murray, N. 2012, MNRAS, 421, 3488, doi: 10.1111/j.1365-2966.2012.20578.x

    doi:10.1111/j.1365-2966.2012.20578.x 2012

  26. [26]

    F., & Raives, M

    Hopkins, P. F., & Raives, M. J. 2016, MNRAS, 455, 51, doi: 10.1093/mnras/stv2180

    doi:10.1093/mnras/stv2180 2016

  27. [27]

    2016, MNRAS, 458, 816, doi: 10.1093/mnras/stw289

    Quataert, E., & Murray, N. 2016, MNRAS, 458, 816, doi: 10.1093/mnras/stw289

    doi:10.1093/mnras/stw289 2016

  28. [28]

    F., Wetzel, A., Kereˇ s, D., et al

    Hopkins, P. F., Wetzel, A., Kereˇ s, D., et al. 2018a, MNRAS, 480, 800, doi: 10.1093/mnras/sty1690 —. 2018b, MNRAS, 477, 1578, doi: 10.1093/mnras/sty674

    doi:10.1093/mnras/sty1690

  29. [29]

    F., Wetzel, A., Wheeler, C., et al

    Hopkins, P. F., Wetzel, A., Wheeler, C., et al. 2023, MNRAS, 519, 3154, doi: 10.1093/mnras/stac3489

    doi:10.1093/mnras/stac3489 2023

  30. [30]

    F., Grudic, M

    Hopkins, P. F., Grudic, M. Y., Su, K.-Y., et al. 2024a, The Open Journal of Astrophysics, 7, 18, doi: 10.21105/astro.2309.13115

    doi:10.21105/astro.2309.13115

  31. [31]

    F., Squire, J., Su, K.-Y., et al

    Hopkins, P. F., Squire, J., Su, K.-Y., et al. 2024b, The Open Journal of Astrophysics, 7, 19, doi: 10.21105/astro.2310.04506

    doi:10.21105/astro.2310.04506

  32. [32]

    F., Su, K.-Y., Murray, N., et al

    Hopkins, P. F., Su, K.-Y., Murray, N., et al. 2025, The Open Journal of Astrophysics, 8, 48, doi: 10.33232/001c.137296

    doi:10.33232/001c.137296 2025

  33. [33]

    Hoyle, F., & Lyttleton, R. A. 1939, Proceedings of the Cambridge Philosophical Society, 35, 405, doi: 10.1017/S0305004100021150

    doi:10.1017/s0305004100021150 1939

  34. [34]

    2020, ARA&A, 58, 27, doi: 10.1146/annurev-astro-120419-014455

    Inayoshi, K., Visbal, E., & Haiman, Z. 2020, ARA&A, 58, 27, doi: 10.1146/annurev-astro-120419-014455

    doi:10.1146/annurev-astro-120419-014455 2020

  35. [35]

    M., & Davis, S

    Jiang, Y.-F., Stone, J. M., & Davis, S. W. 2014, ApJ, 796, 106, doi: 10.1088/0004-637X/796/2/106 —. 2019, ApJ, 880, 67, doi: 10.3847/1538-4357/ab29ff

    doi:10.1088/0004-637x/796/2/106 2014

  36. [36]

    L., & Bromm, V

    Johnson, J. L., & Bromm, V. 2007, MNRAS, 374, 1557, doi: 10.1111/j.1365-2966.2006.11275.x

    doi:10.1111/j.1365-2966.2006.11275.x 2007

  37. [37]

    I., Greene, J

    Kokorev, V., Caputi, K. I., Greene, J. E., et al. 2024, ApJ, 968, 38, doi: 10.3847/1538-4357/ad4265

    doi:10.3847/1538-4357/ad4265 2024

  38. [38]

    S., Silk, J., et al

    Kritos, K., Beckmann, R. S., Silk, J., et al. 2025, ApJ, 991, 58, doi: 10.3847/1538-4357/adeb44

    doi:10.3847/1538-4357/adeb44 2025

  39. [39]

    2002, Science, 295, 82, doi: 10.1126/science.1067524 Lah´ en, N., Naab, T., Johansson, P

    Kroupa, P. 2002, Science, 295, 82, doi: 10.1126/science.1067524 Lah´ en, N., Naab, T., Johansson, P. H., et al. 2020, ApJ, 891, 2, doi: 10.3847/1538-4357/ab7190

    doi:10.1126/science.1067524 2002

  40. [40]

    F., Kelley, L

    Ma, L., Hopkins, P. F., Kelley, L. Z., & Faucher-Gigu` ere, C.-A. 2023, MNRAS, 519, 5543, doi: 10.1093/mnras/stad036

    doi:10.1093/mnras/stad036 2023

  41. [41]

    2014, ApJL, 784, L38, doi: 10.1088/2041-8205/784/2/L38

    Madau, P., Haardt, F., & Dotti, M. 2014, ApJL, 784, L38, doi: 10.1088/2041-8205/784/2/L38

    doi:10.1088/2041-8205/784/2/l38 2014

  42. [42]

    A., & Prole, L

    Mehta, D., Regan, J. A., & Prole, L. 2024, The Open Journal of Astrophysics, 7, 107, doi: 10.33232/001c.126629

    doi:10.33232/001c.126629 2024

  43. [43]

    P., & Marino, A

    Milone, A. P., & Marino, A. F. 2022, Universe, 8, 359, doi: 10.3390/universe8070359 Mu˜ noz-Darias, T., D´ ıaz Trigo, M., Done, C., Ponti, G., &

    doi:10.3390/universe8070359 2022

  44. [44]

    2026, arXiv e-prints, arXiv:2601.05319, doi: 10.48550/arXiv.2601.05319

    Tomaru, R. 2026, arXiv e-prints, arXiv:2601.05319, doi: 10.48550/arXiv.2601.05319

    Pith/arXiv arXiv doi:10.48550/arxiv.2601.05319 2026

  45. [45]

    2025, ApJ, 981, 203, doi: 10.3847/1538-4357/adb1b0

    Matteo, T. 2025, ApJ, 981, 203, doi: 10.3847/1538-4357/adb1b0

    work page doi:10.3847/1538-4357/adb1b0 2025

  46. [46]

    2025, PASP, 137, 034203, doi: 10.1088/1538-3873/adb6d6

    Nagarajan, P., & El-Badry, K. 2025, PASP, 137, 034203, doi: 10.1088/1538-3873/adb6d6

    doi:10.1088/1538-3873/adb6d6 2025

  47. [47]

    T., Costa, G., Girardi, L., et al

    Nguyen, C. T., Costa, G., Girardi, L., et al. 2022, A&A, 665, A126, doi: 10.1051/0004-6361/202244166

    doi:10.1051/0004-6361/202244166 2022

  48. [48]

    2025, MNRAS, 537, 956, doi: 10.1093/mnras/staf002

    Partmann, C., Naab, T., Lah´ en, N., et al. 2025, MNRAS, 537, 956, doi: 10.1093/mnras/staf002

    work page doi:10.1093/mnras/staf002 2025

  49. [49]

    2024, ApJ, 976, 166, doi: 10.3847/1538-4357/ad7732

    Pascale, M., & Dai, L. 2024, ApJ, 976, 166, doi: 10.3847/1538-4357/ad7732

    doi:10.3847/1538-4357/ad7732 2024

  50. [50]

    F., & Tsang, B

    Pascale, M., Dai, L., McKee, C. F., & Tsang, B. T.-H. 2023, ApJ, 957, 77, doi: 10.3847/1538-4357/acf75c Portegies Zwart, S. F., Baumgardt, H., Hut, P., Makino, J., & McMillan, S. L. W. 2004, Nature, 428, 724, doi: 10.1038/nature02448

    doi:10.3847/1538-4357/acf75c 2023

  51. [51]

    1998, A&A, 334, 505, doi: 10.48550/arXiv.astro-ph/9711337

    Portinari, L., Chiosi, C., & Bressan, A. 1998, A&A, 334, 505, doi: 10.48550/arXiv.astro-ph/9711337

    Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9711337 1998

  52. [52]

    2024, MNRAS, 531, 3770, doi: 10.1093/mnras/stae1413

    Rantala, A., Naab, T., & Lah´ en, N. 2024, MNRAS, 531, 3770, doi: 10.1093/mnras/stae1413

    doi:10.1093/mnras/stae1413 2024

  53. [53]

    2024, The Open Journal of Astrophysics, 7, 72, doi: 10.33232/001c.123239

    Regan, J., & Volonteri, M. 2024, The Open Journal of Astrophysics, 7, 72, doi: 10.33232/001c.123239

    doi:10.33232/001c.123239 2024

  54. [54]

    A., & Schleicher, D

    Reinoso, B., Latif, M. A., & Schleicher, D. R. G. 2025, A&A, 700, A66, doi: 10.1051/0004-6361/202554762

    doi:10.1051/0004-6361/202554762 2025

  55. [55]

    M., & Haghi, H

    Ghasemi, S. M., & Haghi, H. 2025, MNRAS, 536, 1332, doi: 10.1093/mnras/stae2644

    work page doi:10.1093/mnras/stae2644 2025

  56. [56]

    F., Faucher-Gigu` ere, C.-A., et al

    Shen, X., Hopkins, P. F., Faucher-Gigu` ere, C.-A., et al. 2020, MNRAS, 495, 3252, doi: 10.1093/mnras/staa1381

    doi:10.1093/mnras/staa1381 2020

  57. [57]

    2025, arXiv e-prints, arXiv:2510.15823, doi: 10.48550/arXiv.2510.15823

    Shi, Y., Dai, L., Murray, N., et al. 2025, arXiv e-prints, arXiv:2510.15823, doi: 10.48550/arXiv.2510.15823

    work page doi:10.48550/arxiv.2510.15823 2025

  58. [58]

    Y., & Hopkins, P

    Shi, Y., Grudi´ c, M. Y., & Hopkins, P. F. 2021, MNRAS, 505, 2753, doi: 10.1093/mnras/stab1470

    work page doi:10.1093/mnras/stab1470 2021

  59. [59]

    Y., Gerling-Dunsmore, H

    Shi, Y., Kremer, K., Grudi´ c, M. Y., Gerling-Dunsmore, H. J., & Hopkins, P. F. 2023, MNRAS, 518, 3606, doi: 10.1093/mnras/stac3245

    doi:10.1093/mnras/stac3245 2023

  60. [60]

    Shi, Y., Kremer, K., & Hopkins, P. F. 2024a, A&A, 691, A24, doi: 10.1051/0004-6361/202450964 —. 2024b, ApJL, 969, L31, doi: 10.3847/2041-8213/ad5a95

    work page doi:10.1051/0004-6361/202450964 2041

  61. [61]

    2005, MNRAS, 361, 776, doi: 10.1111/j.1365-2966.2005.09238.x 15

    Springel, V., Di Matteo, T., & Hernquist, L. 2005, MNRAS, 361, 776, doi: 10.1111/j.1365-2966.2005.09238.x 15

    doi:10.1111/j.1365-2966.2005.09238.x 2005

  62. [62]

    P., et al

    Suh, H., Scharw¨ achter, J., Farina, E. P., et al. 2025, Nature Astronomy, 9, 271, doi: 10.1038/s41550-024-02402-9

    doi:10.1038/s41550-024-02402-9 2025

  63. [63]

    Supermassive Black Hole Growth in Massive Galaxies at Cosmic Dawn

    Sunseri, J., Andalman, Z. L., & Teyssier, R. 2025, arXiv e-prints, arXiv:2510.19822, doi: 10.48550/arXiv.2510.19822

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2510.19822 2025

  64. [64]

    2009, ApJ, 696, 1798, doi: 10.1088/0004-637X/696/2/1798

    Tanaka, T., & Haiman, Z. 2009, ApJ, 696, 1798, doi: 10.1088/0004-637X/696/2/1798

    doi:10.1088/0004-637x/696/2/1798 2009

  65. [65]

    A., Pols, O

    Tout, C. A., Pols, O. R., Eggleton, P. P., & Han, Z. 1996, MNRAS, 281, 257, doi: 10.1093/mnras/281.1.257

    doi:10.1093/mnras/281.1.257 1996

  66. [66]

    2025, Nature Communications, 16, 9830, doi: 10.1038/s41467-025-65070-x

    Tripodi, R., Martis, N., Markov, V., et al. 2025, Nature Communications, 16, 9830, doi: 10.1038/s41467-025-65070-x

    doi:10.1038/s41467-025-65070-x 2025

  67. [67]

    Vink, J. S. 2018, A&A, 615, A119, doi: 10.1051/0004-6361/201832773 —. 2023, A&A, 679, L9, doi: 10.1051/0004-6361/202347827

    doi:10.1051/0004-6361/201832773 2018

  68. [68]

    2021, Nature Reviews Physics, 3, 732, doi: 10.1038/s42254-021-00364-9

    Volonteri, M., Habouzit, M., & Colpi, M. 2021, Nature Reviews Physics, 3, 732, doi: 10.1038/s42254-021-00364-9

    doi:10.1038/s42254-021-00364-9 2021

  69. [69]

    Volonteri, M., & Rees, M. J. 2005, ApJ, 633, 624, doi: 10.1086/466521

    doi:10.1086/466521 2005

  70. [70]

    2021, ApJL, 907, L1, doi: 10.3847/2041-8213/abd8c6

    Wang, F., Yang, J., Fan, X., et al. 2021, ApJL, 907, L1, doi: 10.3847/2041-8213/abd8c6

    doi:10.3847/2041-8213/abd8c6 2021

  71. [71]

    M., White, C

    Zhang, L., Stone, J. M., White, C. J., et al. 2025, arXiv e-prints, arXiv:2509.10638, doi: 10.48550/arXiv.2509.10638

    doi:10.48550/arxiv.2509.10638 2025